Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics
Abstract
:1. Introduction
- Exact Methods: These methods focus on ensuring an optimal solution by exhaustively exploring the entire search space. However, their applicability is limited due to scalability issues. As the complexity of the problem increases, the time required to find an optimal solution increases significantly, which can make them impractical for large-scale problems or those with an excessively large search space.
- Approximate Methods: Unlike exact methods, approximate methods do not guarantee the attainment of an optimal solution. However, they are capable of providing high-quality solutions within reasonable computational times, making them very valuable in practice, especially for complex and large-scale problems. Within this category, metaheuristics are particularly notable. These techniques, which include Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and Ant Colony Optimization (ACO), are known for their ability to find efficient solutions to complex problems through intelligent exploration of the search space, avoiding getting trapped in sub-optimal local solutions.
- Incorporate chaotic maps into binarization schemes to develop chaotic binarization schemes.
- Use these chaotic binarization schemes in three continuous metaheuristics to solve the 0-1 Knapsack Problem.
- Analyze the results obtained in terms of descriptive statistics, convergence, and non-parametric statistical test.
2. Related Work
2.1. Metaheuristics
2.1.1. Sine Cosine Algorithm
2.1.2. Grey Wolf Optimizer
- Alpha (): These are the wolves that lead the pack. In the context of GWO, they represent the current best solution. The alpha guides the search process and decision making during optimization.
- Beta (): These wolves support the alpha and are considered the second-best solution. In the metaheuristic, they assist in directing the search, providing a secondary perspective in the solution space.
- Delta (): Though strong, delta wolves lack leadership skills. They are the third-best solution in the optimization process and contribute to the diversity of the search, bringing variability and preventing the pack (the algorithm) from becoming stagnant.
- Omega (): These wolves are the lowest in the social hierarchy. They have no leadership power and are dedicated to following and protecting the younger members of the pack. In GWO, they represent the other possible solutions, following the lead of the higher-ranking wolves.
Algorithm 1 Sine Cosine Algorithm |
Input: The population Output: The updated population and
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2.1.3. Whale Optimization Algorithm
- Search for the prey: The whales (search agents) explore the solution space to locate the prey (the best solution). Notably in WOA, unlike other metaheuristics, the position update of each search agent is based on a randomly selected agent, not necessarily the best one found so far. This allows for a broader and more diversified exploration of the solution space.
- Encircling the prey: Once the prey (best solution) is identified, the whales position themselves to encircle it. This stage represents an intensification phase, where the algorithm concentrates on the area around the promising solution identified in the search phase.
- Bubble-net attacking: In the final phase, the whales attack the prey using the bubble-net technique. This phase represents a coordinated and focused effort to refine the search in the selected region and optimize the solution.
Algorithm 2 Grey Wolf Optimizer |
Input: The population Output: The updated population and
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2.2. Chaotic Maps
Algorithm 3 Whale Optimization Algorithm |
Input: The population Output: The updated population and
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2.3. Chaotic Maps in Metaheuristics
- Initialization: The implementation of chaotic maps can be effective in creating initial solutions or populations in metaheuristic techniques, thereby replacing the random generation of these solutions. The nature of chaotic dynamics facilitates the distribution of initial solutions in different areas of the search space, thereby enhancing the exploration phase [13,17,18,55,56,57,58,59].
- Local Search: Chaotic maps have the potential to effectively steer the local search process within metaheuristic algorithms. By integrating chaotic dynamics into the metaheuristics, the algorithm gains the ability to break free from local optima and delve into various segments of the solution space [14,50,62,63,64,65,66].
- Parameter Adaptation: Chaos maps can be employed to dynamically adapt the parameters of a metaheuristic. The inherent chaotic behavior aids in the real-time adjustment of metaheuristic-specific parameters such as mutation rates and crossover probabilities in a genetic algorithm, thereby enhancing the algorithm’s adaptability throughout the optimization process [12,19,20,67,68,69,70,71,72,73].
3. Continuous Metaheuristics for Solving Combinatorial Problems
3.1. Two-Step Technique
3.1.1. Transfer Function
3.1.2. Binarization Rule
Algorithm 4 General scheme of continuous MHs for solving combinatorial problems |
Input: The population Output: The updated population and
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4. Proposal: Chaotic Binarization Schemes
Algorithm 5 Chaotic binarization schemes |
Input: The population Output: The updated population and
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5. Experimental Results
5.1. 0-1 Knapsack Problem
5.2. Parameter Setting
5.3. Summary of Results
5.4. Convergence Analysis
5.5. Statistical Test
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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S-Shaped | V-Shaped | ||
---|---|---|---|
Name | Equation | Name | Equation |
S1 | V1 | ||
S2 | V2 | ||
S3 | V3 | ||
S4 | V4 |
Type | Binarization Rules |
---|---|
Standard (STD) | = |
Complement (COM) | = |
Static Probability (SP) | = |
Elitist (ELIT) | = |
Roulette Elitist (ROU_ELIT) | = |
Instance | Number of Items | Optimum |
---|---|---|
knapPI_1_100_1000_1 | 100 | 9147 |
knapPI_1_200_1000_1 | 200 | 11,238 |
knapPI_1_500_1000_1 | 500 | 28,857 |
knapPI_1_1000_1000_1 | 1000 | 54,503 |
knapPI_1_2000_1000_1 | 2000 | 110,625 |
knapPI_2_100_1000_1 | 100 | 1514 |
knapPI_2_200_1000_1 | 200 | 1634 |
knapPI_2_500_1000_1 | 500 | 4566 |
knapPI_2_1000_1000_1 | 1000 | 9052 |
knapPI_2_2000_1000_1 | 2000 | 18,051 |
knapPI_3_100_1000_1 | 100 | 2397 |
knapPI_3_200_1000_1 | 200 | 2697 |
knapPI_3_500_1000_1 | 500 | 7117 |
knapPI_3_1000_1000_1 | 1000 | 14,390 |
knapPI_3_2000_1000_1 | 2000 | 28,919 |
Parameter | Value |
---|---|
Number of metaheuristics | 3 |
Independent runs | 31 |
Transfer Function | S2 (see in Table 1) |
Number of binarization schemes | 24 (see in Figure 5) |
Number of KP instances | 15 (see in Table 3) |
Number of populations | 20 |
Number of iterations | 500 |
parameter a of SCA | 2 |
parameter a of GWO | decreases linearly from 2 to 0 |
parameter a of WOA | decreases linearly from 2 to 0 |
parameter b of WOA | 1 |
Experiment | knapPI_1_100_1000_1 | knapPI_2_100_1000_1 | knapPI_3_100_1000_1 | knapPI_1_200_1000_1 | knapPI_2_200_1000_1 | knapPI_3_200_1000_1 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Op? | MH | Op? | MH | Op? | MH | Op? | MH | Op? | MH | Op? | MH | |
STD_TENT | ✓ | GWO-WOA-SCA | × | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
STD_CIRCLE | ✓ | GWO-WOA-SCA | × | ✓ | GWO-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
STD | ✓ | GWO-WOA-SCA | × | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
STD_SINE | ✓ | GWO-WOA-SCA | × | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
STD_PIECE | ✓ | GWO-WOA-SCA | × | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
STD_LOG | ✓ | GWO-WOA-SCA | × | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
STD_SINU | ✓ | GWO-WOA-SCA | × | WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA |
STD_SINGER | ✓ | GWO-WOA-SCA | × | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
COM | ✓ | GWO-WOA-SCA | × | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
COM_LOG | ✓ | GWO-WOA-SCA | × | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
COM_PIECE | ✓ | GWO-WOA-SCA | × | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
COM_SINE | ✓ | GWO-WOA-SCA | × | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
COM_SINGER | ✓ | GWO-WOA-SCA | × | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
COM_SINU | ✓ | GWO-WOA-SCA | × | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
COM_TENT | ✓ | GWO-WOA-SCA | × | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
COM_CIRCLE | ✓ | GWO-WOA-SCA | × | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
ELIT_SINE | ✓ | GWO-WOA-SCA | × | ✓ | SCA | ✓ | GWO-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | |
ELIT_SINGER | ✓ | GWO-WOA-SCA | × | ✓ | WOA-SCA | ✓ | WOA-SCA | ✓ | GWO-SCA | ✓ | GWO-WOA-SCA | |
ELIT_PIECE | ✓ | GWO-WOA-SCA | × | ✓ | GWO | ✓ | GWO-WOA-SCA | ✓ | WOA-SCA | ✓ | GWO-WOA | |
ELIT_CIRCLE | ✓ | GWO-WOA-SCA | × | ✓ | GWO-WOA | ✓ | GWO-SCA | ✓ | GWO-WOA | ✓ | GWO-SCA | |
ELIT_TENT | ✓ | GWO-WOA-SCA | × | ✓ | SCA | ✓ | WOA | ✓ | GWO-WOA | ✓ | GWO-WOA-SCA | |
ELIT | ✓ | GWO-WOA-SCA | × | × | ✓ | WOA-SCA | ✓ | GWO-WOA | ✓ | WOA-SCA | ||
ELIT_LOG | ✓ | GWO-WOA-SCA | × | ✓ | GWO | ✓ | WOA | ✓ | GWO-SCA | GWO-SCA | ||
ELIT_SINU | ✓ | GWO-WOA-SCA | × | ✓ | WOA | ✓ | GWO | ✓ | GWO-WOA | ✓ | WOA | |
STD_TENT | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | WOA | × | WOA | ✓ | WOA |
STD_CIRCLE | ✓ | GWO-WOA-SCA | ✓ | SCA | ✓ | GWO-WOA-SCA | × | × | WOA | ✓ | WOA | |
STD | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA | × | × | WOA | ✓ | WOA | |
STD_SINE | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA | ✓ | WOA | × | WOA | × | |
STD_PIECE | ✓ | GWO-WOA | ✓ | GWO-WOA-SCA | ✓ | GWO-WOA | ✓ | WOA | × | WOA | × | |
STD_LOG | ✓ | WOA | ✓ | GWO-WOA-SCA | ✓ | WOA | × | × | × | |||
STD_SINU | ✓ | WOA | ✓ | WOA | ✓ | WOA | × | × | × | |||
STD_SINGER | ✓ | WOA | ✓ | WOA | ✓ | WOA | × | × | × | |||
COM | × | × | × | × | × | × | ||||||
COM_LOG | × | × | × | × | × | × | ||||||
COM_PIECE | × | × | × | × | × | × | ||||||
COM_SINE | × | × | × | × | × | × | ||||||
COM_SINGER | × | × | × | × | × | × | ||||||
COM_SINU | × | × | × | × | × | × | ||||||
COM_TENT | × | × | × | × | × | × | ||||||
COM_CIRCLE | × | × | × | × | × | × | ||||||
ELIT_SINE | × | × | × | × | × | × | ||||||
ELIT_SINGER | × | × | × | × | × | × | ||||||
ELIT_PIECE | × | × | × | × | × | × | ||||||
ELIT_CIRCLE | × | × | × | × | × | × | ||||||
ELIT_TENT | × | × | × | × | × | × | ||||||
ELIT | × | × | × | × | × | × | ||||||
ELIT_LOG | × | × | × | × | × | × | ||||||
ELIT_SINU | × | × | × | × | × | × | ||||||
STD_TENT | × | × | × | |||||||||
STD_CIRCLE | × | WOA | × | WOA | × | WOA | ||||||
STD | × | × | × | |||||||||
STD_SINE | × | × | × | |||||||||
STD_PIECE | × | × | × | |||||||||
STD_LOG | × | × | × | |||||||||
STD_SINU | × | × | × | |||||||||
STD_SINGER | × | × | × | |||||||||
COM | × | × | × | |||||||||
COM_LOG | × | × | × | |||||||||
COM_PIECE | × | × | × | |||||||||
COM_SINE | × | × | × | |||||||||
COM_SINGER | × | × | × | |||||||||
COM_SINU | × | × | × | |||||||||
COM_TENT | × | × | × | |||||||||
COM_CIRCLE | × | × | × | |||||||||
ELIT_SINE | × | × | × | |||||||||
ELIT_SINGER | × | × | × | |||||||||
ELIT_PIECE | × | × | × | |||||||||
ELIT_CIRCLE | × | × | × | |||||||||
ELIT_TENT | × | × | × | |||||||||
ELIT | × | × | × | |||||||||
ELIT_LOG | × | × | × | |||||||||
ELIT_SINU | × | × | × |
Experiment | knapPI_1_100_1000_1 | knapPI_2_100_1000_1 | knapPI_3_100_1000_1 | ||||||
---|---|---|---|---|---|---|---|---|---|
Best | Avg. | RPD | Best | Avg. | RPD | Best | Avg. | RPD | |
STD | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_LOG | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_PIECE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_SINE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_SINGER | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_SINU | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_TENT | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_CIRCLE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2396.097 | 0.0 |
COM | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2396.968 | 0.0 |
COM_LOG | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2396.516 | 0.0 |
COM_PIECE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2396.935 | 0.0 |
COM_SINE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2396.71 | 0.0 |
COM_SINGER | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2395.29 | 0.0 |
COM_SINU | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
COM_TENT | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2396.903 | 0.0 |
COM_CIRCLE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2396.29 | 0.0 |
ELIT | 9147.0 | 8903.355 | 0.0 | 1512.0 | 1500.742 | 0.132 | 2396.0 | 2314.71 | 0.042 |
ELIT_LOG | 9147.0 | 8907.677 | 0.0 | 1512.0 | 1502.032 | 0.132 | 2397.0 | 2306.968 | 0.0 |
ELIT_PIECE | 9147.0 | 8910.161 | 0.0 | 1512.0 | 1499.581 | 0.132 | 2397.0 | 2330.419 | 0.0 |
ELIT_SINE | 9147.0 | 8913.871 | 0.0 | 1512.0 | 1499.71 | 0.132 | 2390.0 | 2317.355 | 0.292 |
ELIT_SINGER | 9147.0 | 8868.968 | 0.0 | 1512.0 | 1501.065 | 0.132 | 2396.0 | 2312.677 | 0.042 |
ELIT_SINU | 9147.0 | 8933.355 | 0.0 | 1512.0 | 1501.0 | 0.132 | 2396.0 | 2305.839 | 0.042 |
ELIT_TENT | 9147.0 | 8922.194 | 0.0 | 1512.0 | 1496.29 | 0.132 | 2390.0 | 2308.968 | 0.292 |
ELIT_CIRCLE | 9147.0 | 8914.226 | 0.0 | 1512.0 | 1501.032 | 0.132 | 2397.0 | 2300.452 | 0.0 |
Experiment | knapPI_1_200_1000_1 | knapPI_2_200_1000_1 | knapPI_3_200_1000_1 | ||||||
Best | Avg. | RPD | Best | Avg. | RPD | Best | Avg. | RPD | |
STD | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_LOG | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_PIECE | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_SINE | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_SINGER | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1633.935 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_SINU | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1633.355 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_TENT | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_CIRCLE | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1632.968 | 0.0 | 2697.0 | 2697.0 | 0.0 |
COM | 11,238.0 | 11,237.645 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2696.774 | 0.0 |
COM_LOG | 11,238.0 | 11,233.129 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2696.645 | 0.0 |
COM_PIECE | 11,238.0 | 11,232.548 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2696.871 | 0.0 |
COM_SINE | 11,238.0 | 11,236.581 | 0.0 | 1634.0 | 1633.935 | 0.0 | 2697.0 | 2696.871 | 0.0 |
COM_SINGER | 11,238.0 | 11,201.903 | 0.0 | 1634.0 | 1633.097 | 0.0 | 2697.0 | 2692.323 | 0.0 |
COM_SINU | 11,238.0 | 11,232.677 | 0.0 | 1634.0 | 1630.323 | 0.0 | 2697.0 | 2694.323 | 0.0 |
COM_TENT | 11,238.0 | 11,236.935 | 0.0 | 1634.0 | 1633.935 | 0.0 | 2697.0 | 2696.935 | 0.0 |
COM_CIRCLE | 11,238.0 | 11,228.774 | 0.0 | 1634.0 | 1633.194 | 0.0 | 2697.0 | 2697.0 | 0.0 |
ELIT | 11,227.0 | 10,938.839 | 0.098 | 1634.0 | 1618.452 | 0.0 | 2695.0 | 2637.355 | 0.074 |
ELIT_LOG | 11,227.0 | 10,836.935 | 0.098 | 1634.0 | 1620.484 | 0.0 | 2697.0 | 2640.065 | 0.0 |
ELIT_PIECE | 11,238.0 | 10,882.0 | 0.0 | 1633.0 | 1617.871 | 0.061 | 2697.0 | 2650.581 | 0.0 |
ELIT_SINE | 11,238.0 | 10,855.935 | 0.0 | 1634.0 | 1623.387 | 0.0 | 2697.0 | 2637.516 | 0.0 |
ELIT_SINGER | 11,227.0 | 10,878.613 | 0.098 | 1634.0 | 1614.032 | 0.0 | 2697.0 | 2637.806 | 0.0 |
ELIT_SINU | 11,238.0 | 10,889.871 | 0.0 | 1634.0 | 1619.323 | 0.0 | 2696.0 | 2639.581 | 0.037 |
ELIT_TENT | 11,227.0 | 10,854.161 | 0.098 | 1634.0 | 1615.645 | 0.0 | 2697.0 | 2637.935 | 0.0 |
ELIT_CIRCLE | 11,238.0 | 10,870.516 | 0.0 | 1634.0 | 1618.871 | 0.0 | 2697.0 | 2650.129 | 0.0 |
Experiment | knapPI_1_200_1000_1 | knapPI_2_200_1000_1 | knapPI_3_200_1000_1 | ||||||
Best | Avg. | RPD | Best | Avg. | RPD | Best | Avg. | RPD | |
STD | 28,857.0 | 28,834.774 | 0.0 | 4566.0 | 4561.29 | 0.0 | 7117.0 | 7112.129 | 0.0 |
STD_LOG | 28,834.0 | 28,689.065 | 0.08 | 4566.0 | 4557.355 | 0.0 | 7017.0 | 7016.935 | 1.405 |
STD_PIECE | 28,857.0 | 28,831.258 | 0.0 | 4566.0 | 4566.0 | 0.0 | 7117.0 | 7104.71 | 0.0 |
STD_SINE | 28,857.0 | 28,758.323 | 0.0 | 4566.0 | 4566.0 | 0.0 | 7117.0 | 7062.871 | 0.0 |
STD_SINGER | 28,328.0 | 27,587.419 | 1.833 | 4544.0 | 4516.774 | 0.482 | 6914.0 | 6824.548 | 2.852 |
STD_SINU | 27,513.0 | 26,267.645 | 4.657 | 4534.0 | 4460.935 | 0.701 | 6816.0 | 6664.065 | 4.229 |
STD_TENT | 28,857.0 | 28,829.548 | 0.0 | 4566.0 | 4561.968 | 0.0 | 7117.0 | 7108.29 | 0.0 |
STD_CIRCLE | 28,857.0 | 28,850.323 | 0.0 | 4557.0 | 4551.258 | 0.197 | 7117.0 | 7117.0 | 0.0 |
COM | 28,132.0 | 27,365.097 | 2.512 | 4554.0 | 4503.226 | 0.263 | 6915.0 | 6767.806 | 2.838 |
COM_LOG | 27,389.0 | 26,985.839 | 5.087 | 4514.0 | 4478.548 | 1.139 | 6909.0 | 6734.871 | 2.923 |
COM_PIECE | 28,272.0 | 27,334.839 | 2.027 | 4520.0 | 4497.387 | 1.007 | 6909.0 | 6787.419 | 2.923 |
COM_SINE | 28,164.0 | 27,289.774 | 2.401 | 4541.0 | 4491.871 | 0.548 | 6915.0 | 6774.0 | 2.838 |
COM_SINGER | 27,045.0 | 26,142.387 | 6.279 | 4503.0 | 4439.516 | 1.38 | 6817.0 | 6462.927 | 4.215 |
COM_SINU | 27,483.0 | 26,101.355 | 4.761 | 4492.0 | 4410.032 | 1.621 | 6815.0 | 6659.613 | 4.243 |
COM_TENT | 28,320.0 | 27,390.968 | 1.861 | 4528.0 | 4496.516 | 0.832 | 6915.0 | 6787.0 | 2.838 |
COM_CIRCLE | 27,999.0 | 27,297.935 | 2.973 | 4537.0 | 4506.871 | 0.635 | 7013.0 | 6937.355 | 1.461 |
ELIT | 27,516.0 | 26,179.677 | 4.647 | 4492.0 | 4406.71 | 1.621 | 6916.0 | 6707.613 | 2.824 |
ELIT_LOG | 27,952.0 | 26,336.645 | 3.136 | 4495.0 | 4415.484 | 1.555 | 6812.0 | 6687.968 | 4.286 |
ELIT_PIECE | 27,624.0 | 26,220.355 | 4.273 | 4503.0 | 4409.129 | 1.38 | 6805.0 | 6648.258 | 4.384 |
ELIT_SINE | 27,473.0 | 26,107.548 | 4.796 | 4530.0 | 4416.065 | 0.788 | 6811.0 | 6658.258 | 4.3 |
ELIT_SINGER | 27,238.0 | 25,954.613 | 5.61 | 4532.0 | 4402.0 | 0.745 | 6815.0 | 6678.548 | 4.243 |
ELIT_SINU | 26,995.0 | 26,075.935 | 6.453 | 4486.0 | 4388.645 | 1.752 | 6889.0 | 6661.161 | 3.204 |
ELIT_TENT | 27,007.0 | 25,860.194 | 6.411 | 4500.0 | 4397.452 | 1.445 | 6812.0 | 6653.29 | 4.286 |
ELIT_CIRCLE | 26,947.0 | 25,897.935 | 6.619 | 4482.0 | 4409.484 | 1.84 | 6814.0 | 6676.903 | 4.257 |
Experiment | knapPI_1_1000_1000_1 | knapPI_2_1000_1000_1 | knapPI_3_1000_1000_1 | ||||||
Best | Avg. | RPD | Best | Avg. | RPD | Best | Avg. | RPD | |
STD | 53,838.0 | 53,373.613 | 1.22 | 9030.0 | 9010.29 | 0.243 | 14,189.0 | 14,101.645 | 1.397 |
STD_LOG | 52,617.0 | 52,172.355 | 3.46 | 8997.0 | 8965.71 | 0.608 | 13,988.0 | 13,904.226 | 2.794 |
STD_PIECE | 53,702.0 | 53,227.484 | 1.47 | 9033.0 | 9011.419 | 0.21 | 14,189.0 | 14,101.613 | 1.397 |
STD_SINE | 53,673.0 | 52,915.032 | 1.523 | 9029.0 | 8991.516 | 0.254 | 14,187.0 | 14,067.839 | 1.411 |
STD_SINGER | 49,162.0 | 48,070.29 | 9.799 | 8888.0 | 8778.581 | 1.812 | 13,387.0 | 13,219.484 | 6.97 |
STD_SINU | 48,934.0 | 46,859.129 | 10.218 | 8738.0 | 8594.29 | 3.469 | 13,381.0 | 13,052.452 | 7.012 |
STD_TENT | 53,760.0 | 53,386.548 | 1.363 | 9032.0 | 9006.065 | 0.221 | 14,188.0 | 14,118.032 | 1.404 |
STD_CIRCLE | 54,264.0 | 54,064.484 | 0.439 | 9028.0 | 9011.258 | 0.265 | 14,290.0 | 14,288.0 | 0.695 |
COM | 49,922.0 | 47,741.871 | 8.405 | 8764.0 | 8702.226 | 3.182 | 13,383.0 | 13,128.71 | 6.998 |
COM_LOG | 50,637.0 | 47,340.677 | 7.093 | 8826.0 | 8672.258 | 2.497 | 13,485.0 | 13,076.613 | 6.289 |
COM_PIECE | 49,765.0 | 47,890.452 | 8.693 | 8822.0 | 8697.29 | 2.541 | 13,386.0 | 13,154.032 | 6.977 |
COM_SINE | 49,002.0 | 47,232.645 | 10.093 | 8797.0 | 8681.774 | 2.817 | 13,481.0 | 13,126.613 | 6.317 |
COM_SINGER | 49,632.0 | 46,531.935 | 8.937 | 8765.0 | 8619.419 | 3.171 | 13,383.0 | 13,052.968 | 6.998 |
COM_SINU | 48,900.0 | 46,937.065 | 10.28 | 8699.0 | 8586.387 | 3.9 | 13,467.0 | 13,030.161 | 6.414 |
COM_TENT | 49,271.0 | 47,830.839 | 9.599 | 8806.0 | 8716.194 | 2.718 | 13,283.0 | 13,102.323 | 7.693 |
COM_CIRCLE | 50,789.0 | 50,053.581 | 6.814 | 8869.0 | 8802.742 | 2.022 | 13,789.0 | 13,630.0 | 4.177 |
ELIT | 49,583.0 | 46,430.839 | 9.027 | 8731.0 | 8572.323 | 3.546 | 13,284.0 | 13,036.613 | 7.686 |
ELIT_LOG | 48,212.0 | 46,662.355 | 11.542 | 8767.0 | 8590.935 | 3.148 | 13,386.0 | 13,057.871 | 6.977 |
ELIT_PIECE | 49,049.0 | 46,628.677 | 10.007 | 8789.0 | 8587.355 | 2.905 | 13,178.0 | 13,008.161 | 8.423 |
ELIT_SINE | 48,975.0 | 46,480.968 | 10.143 | 8727.0 | 8574.194 | 3.59 | 13,290.0 | 13,011.452 | 7.644 |
ELIT_SINGER | 49,107.0 | 46,625.387 | 9.9 | 8752.0 | 8591.839 | 3.314 | 13,284.0 | 13,027.484 | 7.686 |
ELIT_SINU | 48,424.0 | 46,412.774 | 11.154 | 8795.0 | 8581.29 | 2.839 | 13,482.0 | 13,062.613 | 6.31 |
ELIT_TENT | 49,590.0 | 46,663.806 | 9.014 | 8753.0 | 8597.032 | 3.303 | 13,285.0 | 12,979.323 | 7.679 |
ELIT_CIRCLE | 48,220.0 | 46,387.839 | 11.528 | 8721.0 | 8580.774 | 3.657 | 13,384.0 | 12,997.484 | 6.991 |
Experiment | knapPI_1_200_1000_1 | knapPI_2_200_1000_1 | knapPI_3_200_1000_1 | ||||||
Best | Avg. | RPD | Best | Avg. | RPD | Best | Avg. | RPD | |
STD | 106,338.0 | 104,652.935 | 3.875 | 17,818.0 | 17,725.677 | 1.291 | 27,910.0 | 27,679.806 | 3.489 |
STD_LOG | 103,254.0 | 101,973.0 | 6.663 | 17,640.0 | 17,548.258 | 2.277 | 27,315.0 | 27,116.548 | 5.547 |
STD_PIECE | 105,308.0 | 104,361.613 | 4.806 | 17,778.0 | 17,704.645 | 1.512 | 27,811.0 | 27,652.323 | 3.831 |
STD_SINE | 104,502.0 | 103,313.387 | 5.535 | 17,706.0 | 17,648.097 | 1.911 | 27,616.0 | 27,408.871 | 4.506 |
STD_SINGER | 94,623.0 | 91,299.226 | 14.465 | 17,081.0 | 16,891.935 | 5.374 | 25,815.0 | 25,341.323 | 10.733 |
STD_SINU | 95,130.0 | 90,711.0 | 14.007 | 16,932.0 | 16,712.71 | 6.199 | 25,818.0 | 25,276.29 | 10.723 |
STD_TENT | 106,008.0 | 105,053.065 | 4.174 | 17,787.0 | 17,711.032 | 1.463 | 28,112.0 | 27,790.548 | 2.791 |
STD_CIRCLE | 108,462.0 | 108,065.452 | 1.955 | 17,970.0 | 17,923.355 | 0.449 | 28,419.0 | 28,334.065 | 1.729 |
COM | 94,380.0 | 90,898.935 | 14.685 | 16,945.0 | 16,804.742 | 6.127 | 25,818.0 | 25,310.355 | 10.723 |
COM_LOG | 95,370.0 | 91,262.032 | 13.79 | 17,215.0 | 16,740.581 | 4.631 | 25,618.0 | 25,276.065 | 11.415 |
COM_PIECE | 95,187.0 | 91,238.548 | 16.219 | 17,048.0 | 16,787.903 | 5.556 | 26,004.0 | 25,338.065 | 10.08 |
COM_SINE | 93,710.0 | 90,704.839 | 15.29 | 17,033.0 | 16,798.935 | 5.64 | 25,909.0 | 25,381.742 | 10.408 |
COM_SINGER | 93,587.0 | 90,654.323 | 15.402 | 17,051.0 | 16,712.903 | 5.54 | 25,616.0 | 25,264.645 | 11.422 |
COM_SINU | 93,509.0 | 90,323.065 | 15.472 | 17,041.0 | 16,731.677 | 5.595 | 26,014.0 | 25,318.71 | 10.045 |
COM_TENT | 95,343.0 | 90,914.774 | 13.814 | 17,029.0 | 16,802.548 | 5.662 | 26,113.0 | 25,271.71 | 9.703 |
COM_CIRCLE | 93,994.0 | 91,883.742 | 15.034 | 17,005.0 | 16,776.258 | 5.795 | 25,818.0 | 25,363.129 | 10.723 |
ELIT | 94,037.0 | 90,814.613 | 14.995 | 16,933.0 | 16,668.71 | 6.194 | 25,619.0 | 25,241.484 | 11.411 |
ELIT_LOG | 93,222.0 | 90,393.161 | 15.732 | 16,984.0 | 16,719.742 | 5.911 | 26,111.0 | 25,367.677 | 9.71 |
ELIT_PIECE | 95,236.0 | 90,678.806 | 13.911 | 17,164.0 | 16,792.129 | 4.914 | 25,806.0 | 25,369.774 | 10.765 |
ELIT_SINE | 94,328.0 | 91,036.806 | 14.732 | 17,000.0 | 16,718.613 | 5.822 | 26,216.0 | 25,342.806 | 9.347 |
ELIT_SINGER | 92,560.0 | 90,297.355 | 16.33 | 16,954.0 | 16,709.871 | 6.077 | 25,619.0 | 25,271.71 | 11.411 |
ELIT_SINU | 93,540.0 | 90,357.613 | 15.444 | 17,129.0 | 16,735.097 | 5.108 | 25,817.0 | 25,296.935 | 10.727 |
ELIT_TENT | 93,337.0 | 90,308.484 | 15.628 | 17,059.0 | 16,700.226 | 5.496 | 25,714.0 | 25,245.452 | 11.083 |
ELIT_CIRCLE | 93,257.0 | 90,411.548 | 15.7 | 16,992.0 | 16,732.355 | 5.867 | 25,916.0 | 25,247.839 | 10.384 |
Experiment | knapPI_1_100_1000_1 | knapPI_2_100_1000_1 | knapPI_3_100_1000_1 | ||||||
---|---|---|---|---|---|---|---|---|---|
Best | Avg. | RPD | Best | Avg. | RPD | Best | Avg. | RPD | |
STD | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_LOG | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_PIECE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_SINE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_SINGER | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_SINU | 9147.0 | 9147.0 | 0.0 | 1513.0 | 1512.097 | 0.066 | 2397.0 | 2397.0 | 0.0 |
STD_TENT | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_CIRCLE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2396.0 | 2396.0 | 0.042 |
COM | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2396.968 | 0.0 |
COM_LOG | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2396.903 | 0.0 |
COM_PIECE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2396.968 | 0.0 |
COM_SINE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2396.935 | 0.0 |
COM_SINGER | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2396.935 | 0.0 |
COM_SINU | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1509.871 | 0.132 | 2397.0 | 2397.0 | 0.0 |
COM_TENT | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2396.968 | 0.0 |
COM_CIRCLE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2396.968 | 0.0 |
ELIT | 9147.0 | 8855.355 | 0.0 | 1512.0 | 1499.548 | 0.132 | 2396.0 | 2313.226 | 0.042 |
ELIT_LOG | 9147.0 | 8930.355 | 0.0 | 1512.0 | 1498.484 | 0.132 | 2390.0 | 2322.226 | 0.292 |
ELIT_PIECE | 9147.0 | 8971.774 | 0.0 | 1512.0 | 1495.161 | 0.132 | 2396.0 | 2312.387 | 0.042 |
ELIT_SINE | 9147.0 | 8925.742 | 0.0 | 1512.0 | 1499.161 | 0.132 | 2396.0 | 2309.226 | 0.042 |
ELIT_SINGER | 9147.0 | 8886.419 | 0.0 | 1512.0 | 1498.516 | 0.132 | 2397.0 | 2313.194 | 0.0 |
ELIT_SINU | 9147.0 | 8912.452 | 0.0 | 1512.0 | 1498.161 | 0.132 | 2397.0 | 2306.839 | 0.0 |
Experiment | knapPI_1_200_1000_1 | knapPI_2_200_1000_1 | knapPI_3_200_1000_1 | ||||||
Best | Avg. | RPD | Best | Avg. | RPD | Best | Avg. | RPD | |
ELIT_TENT | 9147.0 | 8876.065 | 0.0 | 1512.0 | 1495.903 | 0.132 | 2390.0 | 2326.903 | 0.292 |
ELIT_CIRCLE | 9147.0 | 8863.613 | 0.0 | 1512.0 | 1497.645 | 0.132 | 2397.0 | 2305.677 | 0.0 |
STD | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_LOG | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_PIECE | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_SINE | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_SINGER | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_SINU | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_TENT | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_CIRCLE | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
COM | 11,238.0 | 11,236.935 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
COM_LOG | 11,238.0 | 11,235.871 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2696.871 | 0.0 |
COM_PIECE | 11,238.0 | 11,236.226 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2696.968 | 0.0 |
COM_SINE | 11,238.0 | 11,236.097 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2696.871 | 0.0 |
COM_SINGER | 11,238.0 | 11,233.484 | 0.0 | 1634.0 | 1633.516 | 0.0 | 2697.0 | 2696.032 | 0.0 |
COM_SINU | 11,238.0 | 11,236.581 | 0.0 | 1634.0 | 1629.71 | 0.0 | 2697.0 | 2696.645 | 0.0 |
COM_TENT | 11,238.0 | 11,237.645 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
COM_CIRCLE | 11,238.0 | 11,233.742 | 0.0 | 1634.0 | 1633.548 | 0.0 | 2697.0 | 2697.0 | 0.0 |
ELIT | 11,238.0 | 10,900.387 | 0.0 | 1634.0 | 1617.065 | 0.0 | 2697.0 | 2657.032 | 0.0 |
ELIT_LOG | 11,238.0 | 10,874.161 | 0.0 | 1633.0 | 1615.129 | 0.061 | 2694.0 | 2626.774 | 0.111 |
ELIT_PIECE | 11,238.0 | 10,862.226 | 0.0 | 1634.0 | 1617.161 | 0.0 | 2697.0 | 2639.0 | 0.0 |
ELIT_SINE | 11,227.0 | 10,839.29 | 0.098 | 1634.0 | 1617.323 | 0.0 | 2697.0 | 2642.065 | 0.0 |
ELIT_SINGER | 11,238.0 | 10,919.548 | 0.0 | 1633.0 | 1616.935 | 0.061 | 2697.0 | 2659.355 | 0.0 |
ELIT_SINU | 11,223.0 | 10,896.516 | 0.133 | 1634.0 | 1613.613 | 0.0 | 2697.0 | 2648.387 | 0.0 |
ELIT_TENT | 11,238.0 | 10,782.806 | 0.0 | 1634.0 | 1617.0 | 0.0 | 2697.0 | 2658.355 | 0.0 |
ELIT_CIRCLE | 11,227.0 | 10,790.129 | 0.098 | 1634.0 | 1621.032 | 0.0 | 2695.0 | 2628.258 | 0.074 |
Experiment | knapPI_1_500_1000_1 | knapPI_2_500_1000_1 | knapPI_3_500_1000_1 | ||||||
Best | Avg. | RPD | Best | Avg. | RPD | Best | Avg. | RPD | |
STD | 28,857.0 | 28,856.258 | 0.0 | 4566.0 | 4565.484 | 0.0 | 7117.0 | 7117.0 | 0.0 |
STD_LOG | 28,857.0 | 28,845.871 | 0.0 | 4566.0 | 4565.613 | 0.0 | 7117.0 | 7116.903 | 0.0 |
STD_PIECE | 28,857.0 | 28,856.258 | 0.0 | 4566.0 | 4566.0 | 0.0 | 7117.0 | 7117.0 | 0.0 |
STD_SINE | 28,857.0 | 28,849.581 | 0.0 | 4566.0 | 4565.548 | 0.0 | 7117.0 | 7117.0 | 0.0 |
STD_SINGER | 28,857.0 | 28,759.29 | 0.0 | 4566.0 | 4557.774 | 0.0 | 7117.0 | 7051.226 | 0.0 |
STD_SINU | 28,857.0 | 28,674.71 | 0.0 | 4566.0 | 4560.839 | 0.0 | 7117.0 | 7023.032 | 0.0 |
STD_TENT | 28,857.0 | 28,853.29 | 0.0 | 4566.0 | 4566.0 | 0.0 | 7117.0 | 7117.0 | 0.0 |
STD_CIRCLE | 28,857.0 | 28,834.742 | 0.0 | 4552.0 | 4551.29 | 0.307 | 7117.0 | 7117.0 | 0.0 |
COM | 28,076.0 | 27,386.677 | 2.706 | 4555.0 | 4507.968 | 0.241 | 6913.0 | 6790.355 | 2.866 |
COM_LOG | 27,788.0 | 27,144.065 | 3.704 | 4549.0 | 4491.581 | 0.372 | 6912.0 | 6755.129 | 2.88 |
COM_PIECE | 28,108.0 | 27,405.774 | 2.596 | 4529.0 | 4500.387 | 0.81 | 6917.0 | 6804.839 | 2.81 |
COM_SINE | 27,953.0 | 27,397.419 | 3.133 | 4533.0 | 4501.452 | 0.723 | 6900.0 | 6788.355 | 3.049 |
COM_SINGER | 27,972.0 | 26,589.097 | 3.067 | 4513.0 | 4458.452 | 1.161 | 6908.0 | 6699.258 | 2.937 |
COM_SINU | 27,347.0 | 26,271.161 | 5.233 | 4525.0 | 4452.161 | 0.898 | 6817.0 | 6677.484 | 4.215 |
COM_TENT | 28,173.0 | 27,497.774 | 2.37 | 4555.0 | 4507.581 | 0.241 | 6901.0 | 6788.194 | 3.035 |
COM_CIRCLE | 28,247.0 | 27,596.935 | 2.114 | 4551.0 | 4507.581 | 0.329 | 6998.0 | 6816.0 | 1.672 |
ELIT | 27,670.0 | 26,169.129 | 4.113 | 4509.0 | 4402.355 | 1.248 | 6904.0 | 6681.935 | 2.993 |
ELIT_LOG | 28,187.0 | 26,043.774 | 2.322 | 4526.0 | 4418.613 | 0.876 | 6908.0 | 6671.097 | 2.937 |
ELIT_PIECE | 27,241.0 | 25,960.355 | 5.6 | 4472.0 | 4400.323 | 2.059 | 6816.0 | 6660.097 | 4.229 |
ELIT_SINE | 27,318.0 | 25,972.29 | 5.333 | 4507.0 | 4398.548 | 1.292 | 7016.0 | 6664.806 | 1.419 |
ELIT_SINGER | 27,655.0 | 25,919.452 | 4.165 | 4535.0 | 4414.355 | 0.679 | 6815.0 | 6666.581 | 4.243 |
ELIT_SINU | 27,717.0 | 26,085.613 | 3.951 | 4486.0 | 4399.161 | 1.752 | 6808.0 | 6666.968 | 4.342 |
ELIT_TENT | 27,442.0 | 26,103.839 | 4.903 | 4508.0 | 4410.71 | 1.27 | 6908.0 | 6653.355 | 2.937 |
ELIT_CIRCLE | 27,296.0 | 26,013.194 | 5.409 | 4473.0 | 4402.774 | 2.037 | 6914.0 | 6663.935 | 2.852 |
Experiment | knapPI_1_200_1000_1 | knapPI_2_200_1000_1 | knapPI_3_200_1000_1 | ||||||
Best | Avg. | RPD | Best | Avg. | RPD | Best | Avg. | RPD | |
STD | 54,485.0 | 54,352.774 | 0.033 | 9051.0 | 9050.0 | 0.011 | 14,390.0 | 14,329.871 | 0.0 |
STD_LOG | 54,205.0 | 53,928.097 | 0.547 | 9048.0 | 9031.484 | 0.044 | 14,290.0 | 14,235.903 | 0.695 |
STD_PIECE | 54,503.0 | 54,370.194 | 0.0 | 9051.0 | 9049.323 | 0.011 | 14,389.0 | 14,326.258 | 0.007 |
STD_SINE | 54,503.0 | 54,118.871 | 0.0 | 9051.0 | 9043.387 | 0.011 | 14,290.0 | 14,280.29 | 0.695 |
STD_SINGER | 53,458.0 | 52,809.032 | 1.917 | 9027.0 | 8989.645 | 0.276 | 14,186.0 | 14,053.226 | 1.418 |
STD_SINU | 52,687.0 | 52,146.323 | 3.332 | 9006.0 | 8968.806 | 0.508 | 13,989.0 | 13,873.645 | 2.787 |
STD_TENT | 54,503.0 | 54,371.0 | 0.0 | 9051.0 | 9049.774 | 0.011 | 14,390.0 | 14,311.806 | 0.0 |
STD_CIRCLE | 54,481.0 | 54,475.355 | 0.04 | 9051.0 | 9049.839 | 0.011 | 14,390.0 | 14,389.613 | 0.0 |
COM | 49,135.0 | 48,006.0 | 9.849 | 8893.0 | 8746.484 | 1.757 | 13,469.0 | 13,161.645 | 6.4 |
COM_LOG | 48,767.0 | 47,592.226 | 10.524 | 8826.0 | 8701.516 | 2.497 | 13,290.0 | 13,084.032 | 7.644 |
COM_PIECE | 49,832.0 | 47,974.226 | 8.57 | 8810.0 | 8745.871 | 2.673 | 13,489.0 | 13,176.032 | 6.261 |
COM_SINE | 49,312.0 | 47,966.194 | 9.524 | 8790.0 | 8716.516 | 2.894 | 13,486.0 | 13,178.161 | 6.282 |
COM_SINGER | 50,170.0 | 46,691.161 | 7.95 | 8758.0 | 8609.71 | 3.248 | 13,375.0 | 13,009.419 | 7.054 |
COM_SINU | 49,464.0 | 46,881.032 | 9.245 | 8830.0 | 8558.516 | 2.452 | 13,282.0 | 13,046.548 | 7.7 |
COM_TENT | 49,743.0 | 48,183.645 | 8.733 | 8944.0 | 8746.258 | 1.193 | 13,366.0 | 13,131.194 | 7.116 |
COM_CIRCLE | 50,372.0 | 49,047.355 | 7.579 | 8879.0 | 8778.226 | 1.911 | 13,985.0 | 13,426.806 | 2.814 |
ELIT | 48,421.0 | 46,461.742 | 11.159 | 8720.0 | 8592.29 | 3.668 | 13,385.0 | 12,983.839 | 6.984 |
ELIT_LOG | 48,497.0 | 46,619.903 | 11.02 | 8677.0 | 8571.258 | 4.143 | 13,482.0 | 13,058.968 | 6.31 |
ELIT_PIECE | 49,052.0 | 46,461.161 | 10.001 | 8748.0 | 8592.935 | 3.358 | 13,283.0 | 13,043.839 | 7.693 |
ELIT_SINE | 48,976.0 | 46,446.516 | 10.141 | 8734.0 | 8589.516 | 3.513 | 13,284.0 | 13,009.484 | 7.686 |
ELIT_SINGER | 49,767.0 | 46,828.258 | 8.689 | 8737.0 | 8577.903 | 3.48 | 13,289.0 | 12,997.258 | 7.651 |
ELIT_SINU | 47,838.0 | 46,475.677 | 12.229 | 8732.0 | 8570.419 | 3.535 | 13,484.0 | 13,036.645 | 6.296 |
ELIT_TENT | 49,784.0 | 47,014.29 | 8.658 | 8802.0 | 8590.774 | 2.762 | 13,482.0 | 13,055.194 | 6.31 |
ELIT_CIRCLE | 49,289.0 | 46,553.29 | 9.566 | 8780.0 | 8597.194 | 3.005 | 13,380.0 | 13,045.323 | 7.019 |
Experiment | knapPI_1_2000_1000_1 | knapPI_2_2000_1000_1 | knapPI_3_2000_1000_1 | ||||||
Best | Avg. | RPD | Best | Avg. | RPD | Best | Avg. | RPD | |
STD | 109,623.0 | 108,875.903 | 0.906 | 18,027.0 | 17,969.613 | 0.133 | 28,809.0 | 28,617.29 | 0.38 |
STD_LOG | 108,467.0 | 106,985.742 | 1.951 | 17,960.0 | 17,877.871 | 0.504 | 28,319.0 | 28,210.032 | 2.075 |
STD_PIECE | 109,791.0 | 105,507.292 | 0.754 | 18,022.0 | 17,971.806 | 0.161 | 28,713.0 | 28,583.806 | 0.712 |
STD_SINE | 108,598.0 | 107,846.419 | 1.832 | 17,981.0 | 17,905.161 | 0.388 | 28,519.0 | 28,376.161 | 1.383 |
STD_SINGER | 104,903.0 | 103,691.387 | 5.172 | 17,774.0 | 17,658.903 | 1.535 | 27,808.0 | 27,553.613 | 3.842 |
STD_SINU | 103,389.0 | 100,545.613 | 6.541 | 17,626.0 | 17,501.968 | 2.354 | 27,416.0 | 26,964.774 | 5.197 |
STD_TENT | 109,959.0 | 109,113.226 | 0.602 | 18,009.0 | 17,968.452 | 0.233 | 28,719.0 | 28,603.677 | 0.692 |
STD_CIRCLE | 110,555.0 | 110,214.419 | 0.063 | 18,040.0 | 18,027.323 | 0.061 | 28,916.0 | 28,830.774 | 0.01 |
COM | 95,052.0 | 91,784.613 | 14.077 | 16,984.0 | 16,814.29 | 5.911 | 25,916.0 | 25,383.806 | 10.384 |
COM_LOG | 92,635.0 | 90,981.419 | 16.262 | 17,062.0 | 16,795.645 | 5.479 | 25,811.0 | 25,221.323 | 10.747 |
COM_PIECE | 94,761.0 | 91,531.484 | 14.34 | 17,279.0 | 16,832.194 | 4.277 | 25,718.0 | 25,318.677 | 11.069 |
COM_SINE | 94,146.0 | 91,178.806 | 14.896 | 17,068.0 | 16,805.871 | 5.446 | 25,906.0 | 25,271.258 | 10.419 |
COM_SINGER | 95,646.0 | 90,601.161 | 13.54 | 17,031.0 | 16,735.548 | 5.651 | 25,811.0 | 25,342.323 | 10.747 |
COM_SINU | 96,128.0 | 90,695.226 | 13.105 | 17,133.0 | 16,728.935 | 5.086 | 26,015.0 | 25,274.387 | 10.042 |
COM_TENT | 95,027.0 | 91,353.129 | 14.1 | 17,092.0 | 16,850.774 | 5.313 | 25,715.0 | 25,332.645 | 11.079 |
COM_CIRCLE | 95,741.0 | 92,354.161 | 13.454 | 17,083.0 | 16,874.71 | 5.363 | 25,815.0 | 25,367.129 | 10.733 |
ELIT | 93,971.0 | 90,895.742 | 15.054 | 16,969.0 | 16,727.032 | 5.994 | 26,418.0 | 25,331.742 | 8.648 |
ELIT_LOG | 94,071.0 | 90,695.968 | 14.964 | 16,990.0 | 16,759.129 | 5.878 | 25,809.0 | 25,297.194 | 10.754 |
ELIT_PIECE | 94,861.0 | 90,753.613 | 14.25 | 17,039.0 | 16,728.516 | 5.606 | 25,818.0 | 25,361.548 | 10.723 |
ELIT_SINE | 93,616.0 | 90,590.871 | 15.375 | 17,009.0 | 16,753.613 | 5.773 | 26,011.0 | 25,300.258 | 10.056 |
ELIT_SINGER | 95,689.0 | 90,577.935 | 13.501 | 16,957.0 | 16,700.935 | 6.061 | 26,010.0 | 25,305.419 | 10.059 |
ELIT_SINU | 93,962.0 | 90,689.613 | 15.063 | 17,135.0 | 16,696.968 | 5.075 | 25,611.0 | 25,230.226 | 11.439 |
ELIT_TENT | 94,309.0 | 90,461.419 | 14.749 | 16,990.0 | 16,707.387 | 5.878 | 25,910.0 | 25,360.452 | 10.405 |
ELIT_CIRCLE | 93,525.0 | 90,443.548 | 15.458 | 17,124.0 | 16,765.419 | 5.135 | 26,013.0 | 25,284.032 | 10.049 |
Experiment | knapPI_1_100_1000_1 | knapPI_2_100_1000_1 | knapPI_3_100_1000_1 | ||||||
---|---|---|---|---|---|---|---|---|---|
Best | Avg. | RPD | Best | Avg. | RPD | Best | Avg. | RPD | |
STD | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_LOG | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_PIECE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_SINE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_SINGER | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_SINU | 9147.0 | 9147.0 | 0.0 | 1513.0 | 1512.032 | 0.066 | 2397.0 | 2397.0 | 0.0 |
STD_TENT | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2397.0 | 0.0 |
STD_CIRCLE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2396.097 | 0.0 |
COM | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2395.387 | 0.0 |
COM_LOG | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2393.968 | 0.0 |
COM_PIECE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2392.677 | 0.0 |
COM_SINE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2395.226 | 0.0 |
COM_SINGER | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2381.129 | 0.0 |
COM_SINU | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1501.935 | 0.132 | 2397.0 | 2397.0 | 0.0 |
COM_TENT | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2395.548 | 0.0 |
COM_CIRCLE | 9147.0 | 9147.0 | 0.0 | 1512.0 | 1512.0 | 0.132 | 2397.0 | 2393.677 | 0.0 |
ELIT | 9147.0 | 8815.935 | 0.0 | 1512.0 | 1499.065 | 0.132 | 2390.0 | 2301.742 | 0.292 |
ELIT_LOG | 9147.0 | 8898.839 | 0.0 | 1512.0 | 1500.452 | 0.132 | 2396.0 | 2316.452 | 0.042 |
ELIT_PIECE | 9147.0 | 8938.839 | 0.0 | 1512.0 | 1493.516 | 0.132 | 2396.0 | 2319.29 | 0.042 |
ELIT_SINE | 9147.0 | 8889.323 | 0.0 | 1512.0 | 1498.258 | 0.132 | 2397.0 | 2311.419 | 0.0 |
ELIT_SINGER | 9147.0 | 8904.613 | 0.0 | 1512.0 | 1498.387 | 0.132 | 2397.0 | 2324.387 | 0.0 |
ELIT_SINU | 9147.0 | 8942.323 | 0.0 | 1512.0 | 1501.903 | 0.132 | 2396.0 | 2316.71 | 0.042 |
ELIT_TENT | 9147.0 | 8872.839 | 0.0 | 1512.0 | 1498.323 | 0.132 | 2397.0 | 2326.645 | 0.0 |
ELIT_CIRCLE | 9147.0 | 8893.484 | 0.0 | 1512.0 | 1496.0 | 0.132 | 2390.0 | 2310.581 | 0.292 |
Experiment | knapPI_1_200_1000_1 | knapPI_2_200_1000_1 | knapPI_3_200_1000_1 | ||||||
Best | Avg. | RPD | Best | Avg. | RPD | Best | Avg. | RPD | |
STD | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_LOG | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_PIECE | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_SINE | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_SINGER | 11,238.0 | 11,237.645 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_SINU | 11,238.0 | 11,237.29 | 0.0 | 1634.0 | 1631.419 | 0.0 | 2697.0 | 2696.677 | 0.0 |
STD_TENT | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
STD_CIRCLE | 11,238.0 | 11,238.0 | 0.0 | 1634.0 | 1634.0 | 0.0 | 2697.0 | 2697.0 | 0.0 |
COM | 11,238.0 | 11,217.71 | 0.0 | 1634.0 | 1633.548 | 0.0 | 2697.0 | 2695.484 | 0.0 |
COM_LOG | 11,238.0 | 11,212.742 | 0.0 | 1634.0 | 1633.258 | 0.0 | 2697.0 | 2695.871 | 0.0 |
COM_PIECE | 11,238.0 | 11,217.71 | 0.0 | 1634.0 | 1633.806 | 0.0 | 2697.0 | 2695.226 | 0.0 |
COM_SINE | 11,238.0 | 11,231.613 | 0.0 | 1634.0 | 1633.742 | 0.0 | 2697.0 | 2695.774 | 0.0 |
COM_SINGER | 11,238.0 | 11,120.194 | 0.0 | 1634.0 | 1632.484 | 0.0 | 2697.0 | 2656.516 | 0.0 |
COM_SINU | 11,238.0 | 11,231.613 | 0.0 | 1634.0 | 1628.032 | 0.0 | 2697.0 | 2693.645 | 0.0 |
COM_TENT | 11,238.0 | 11,226.548 | 0.0 | 1634.0 | 1633.452 | 0.0 | 2697.0 | 2695.387 | 0.0 |
COM_CIRCLE | 11,238.0 | 11,137.839 | 0.0 | 1634.0 | 1630.613 | 0.0 | 2697.0 | 2693.387 | 0.0 |
ELIT | 11,238.0 | 10,875.645 | 0.0 | 1627.0 | 1615.903 | 0.428 | 2697.0 | 2660.226 | 0.0 |
ELIT_LOG | 11,227.0 | 10,865.968 | 0.098 | 1634.0 | 1616.839 | 0.0 | 2697.0 | 2643.903 | 0.0 |
ELIT_PIECE | 11,238.0 | 10,837.29 | 0.0 | 1634.0 | 1621.516 | 0.0 | 2695.0 | 2659.258 | 0.074 |
ELIT_SINE | 11,238.0 | 10,874.677 | 0.0 | 1634.0 | 1618.323 | 0.0 | 2697.0 | 2633.581 | 0.0 |
ELIT_SINGER | 11,238.0 | 10,952.065 | 0.0 | 1634.0 | 1617.742 | 0.0 | 2697.0 | 2655.097 | 0.0 |
ELIT_SINU | 11,183.0 | 10,892.226 | 0.489 | 1633.0 | 1619.0 | 0.061 | 2695.0 | 2641.065 | 0.074 |
ELIT_TENT | 11,227.0 | 10,868.484 | 0.098 | 1627.0 | 1613.806 | 0.428 | 2697.0 | 2648.839 | 0.0 |
ELIT_CIRCLE | 11,238.0 | 10,880.548 | 0.0 | 1627.0 | 1616.226 | 0.428 | 2697.0 | 2645.032 | 0.0 |
Experiment | knapPI_1_200_1000_1 | knapPI_2_200_1000_1 | knapPI_3_200_1000_1 | ||||||
Best | Avg. | RPD | Best | Avg. | RPD | Best | Avg. | RPD | |
STD | 28,857.0 | 28,772.323 | 0.0 | 4566.0 | 4558.548 | 0.0 | 7116.0 | 7069.935 | 0.014 |
STD_LOG | 28,764.0 | 28,625.194 | 0.322 | 4566.0 | 4554.129 | 0.0 | 7017.0 | 7016.355 | 1.405 |
STD_PIECE | 28,834.0 | 28,791.613 | 0.08 | 4566.0 | 4560.484 | 0.0 | 7116.0 | 7058.968 | 0.014 |
STD_SINE | 28,857.0 | 28,706.935 | 0.0 | 4566.0 | 4566.0 | 0.0 | 7116.0 | 7025.645 | 0.014 |
STD_SINGER | 28,182.0 | 27,467.387 | 2.339 | 4551.0 | 4507.968 | 0.329 | 6915.0 | 6815.968 | 2.838 |
STD_SINU | 27,261.0 | 26,158.355 | 5.531 | 4501.0 | 4437.484 | 1.424 | 6815.0 | 6658.032 | 4.243 |
STD_TENT | 28,857.0 | 28,793.935 | 0.0 | 4566.0 | 4561.355 | 0.0 | 7117.0 | 7087.71 | 0.0 |
STD_CIRCLE | 28,857.0 | 28,855.516 | 0.0 | 4566.0 | 4554.613 | 0.0 | 7117.0 | 7117.0 | 0.0 |
COM | 27,534.0 | 26,586.032 | 4.585 | 4505.0 | 4454.323 | 1.336 | 6814.0 | 6672.742 | 4.257 |
COM_LOG | 26,993.0 | 26,440.452 | 6.459 | 4499.0 | 4456.452 | 1.467 | 6815.0 | 6692.516 | 4.243 |
COM_PIECE | 27,409.0 | 26,451.419 | 5.018 | 4512.0 | 4451.871 | 1.183 | 6817.0 | 6675.806 | 4.215 |
COM_SINE | 27,353.0 | 26,598.194 | 5.212 | 4517.0 | 4455.387 | 1.073 | 6817.0 | 6708.0 | 4.215 |
COM_SINGER | 27,610.0 | 26,059.645 | 4.321 | 4497.0 | 4413.29 | 1.511 | 6806.0 | 6657.226 | 4.37 |
COM_SINU | 27,051.0 | 26,021.871 | 6.258 | 4459.0 | 4394.161 | 2.343 | 6817.0 | 6663.935 | 4.215 |
COM_TENT | 27,446.0 | 26,551.226 | 4.89 | 4537.0 | 4455.71 | 0.635 | 6816.0 | 6699.194 | 4.229 |
COM_CIRCLE | 27,201.0 | 26,517.323 | 5.739 | 4507.0 | 4442.065 | 1.292 | 6913.0 | 6699.226 | 2.866 |
ELIT | 27,088.0 | 26,168.129 | 6.13 | 4509.0 | 4402.129 | 1.248 | 6916.0 | 6664.0 | 2.824 |
ELIT_LOG | 27,540.0 | 26,029.226 | 4.564 | 4504.0 | 4414.387 | 1.358 | 6816.0 | 6684.484 | 4.229 |
ELIT_PIECE | 27,207.0 | 26,009.161 | 5.718 | 4515.0 | 4410.29 | 1.117 | 6813.0 | 6661.258 | 4.271 |
ELIT_SINE | 27,046.0 | 25,994.484 | 6.276 | 4514.0 | 4409.032 | 1.139 | 6815.0 | 6675.387 | 4.243 |
ELIT_SINGER | 26,614.0 | 25,867.839 | 7.773 | 4479.0 | 4412.935 | 1.905 | 6910.0 | 6680.516 | 2.909 |
ELIT_SINU | 27,665.0 | 26,207.032 | 4.131 | 4533.0 | 4409.806 | 0.723 | 6796.0 | 6656.484 | 4.51 |
ELIT_TENT | 27,248.0 | 26,044.806 | 5.576 | 4491.0 | 4409.097 | 1.643 | 7015.0 | 6654.484 | 1.433 |
ELIT_CIRCLE | 27,270.0 | 26,108.871 | 5.5 | 4483.0 | 4395.677 | 1.818 | 6903.0 | 6669.613 | 3.007 |
Experiment | knapPI_1_1000_1000_1 | knapPI_2_1000_1000_1 | knapPI_3_1000_1000_1 | ||||||
Best | Avg. | RPD | Best | Avg. | RPD | Best | Avg. | RPD | |
STD | 53,681.0 | 52,958.129 | 1.508 | 9045.0 | 8989.871 | 0.077 | 14,090.0 | 14,039.097 | 2.085 |
STD_LOG | 52,931.0 | 51,803.355 | 2.884 | 9001.0 | 8947.581 | 0.563 | 13,990.0 | 13,867.774 | 2.78 |
STD_PIECE | 53,662.0 | 52,702.71 | 1.543 | 9030.0 | 8988.258 | 0.243 | 14,090.0 | 14,030.516 | 2.085 |
STD_SINE | 53,318.0 | 52,691.935 | 2.174 | 9013.0 | 8987.806 | 0.431 | 14,087.0 | 13,987.065 | 2.106 |
STD_SINGER | 49,265.0 | 47,890.0 | 9.61 | 8827.0 | 8744.71 | 2.486 | 13,467.0 | 13,186.645 | 6.414 |
STD_SINU | 48,741.0 | 46,592.0 | 10.572 | 8729.0 | 8589.258 | 3.568 | 13,286.0 | 13,046.0 | 7.672 |
STD_TENT | 53,416.0 | 52,875.29 | 1.994 | 9028.0 | 8988.226 | 0.265 | 14,187.0 | 14,056.677 | 1.411 |
STD_CIRCLE | 54,234.0 | 54,057.452 | 0.494 | 9030.0 | 9013.968 | 0.243 | 14,290.0 | 14,285.226 | 0.695 |
COM | 49,110.0 | 46,767.677 | 9.895 | 8718.0 | 8611.258 | 3.69 | 13,388.0 | 13,052.645 | 6.963 |
COM_LOG | 48,051.0 | 46,850.258 | 11.838 | 8837.0 | 8614.419 | 2.375 | 13,384.0 | 13,069.774 | 6.991 |
COM_PIECE | 48,216.0 | 46,511.387 | 11.535 | 8712.0 | 8603.774 | 3.756 | 13,276.0 | 13,000.548 | 7.741 |
COM_SINE | 48,435.0 | 46,890.097 | 11.133 | 8784.0 | 8630.032 | 2.961 | 13,383.0 | 13,054.065 | 6.998 |
COM_SINGER | 48,477.0 | 46,364.194 | 11.056 | 8759.0 | 8601.065 | 3.237 | 13,490.0 | 13,031.903 | 6.254 |
COM_SINU | 47,996.0 | 46,647.258 | 11.939 | 8815.0 | 8588.613 | 2.618 | 13,377.0 | 13,040.097 | 7.04 |
COM_TENT | 48,867.0 | 46,575.839 | 10.341 | 8769.0 | 8616.032 | 3.126 | 13,390.0 | 13,008.29 | 6.949 |
COM_CIRCLE | 48,510.0 | 47,243.968 | 10.996 | 8753.0 | 8654.065 | 3.303 | 13,287.0 | 13,034.613 | 7.665 |
ELIT | 48,700.0 | 46,472.032 | 10.647 | 8684.0 | 8579.0 | 4.065 | 13,378.0 | 13,041.419 | 7.033 |
ELIT_LOG | 49,297.0 | 46,567.968 | 9.552 | 8752.0 | 8601.355 | 3.314 | 13,478.0 | 13,063.097 | 6.338 |
ELIT_PIECE | 48,445.0 | 46,666.29 | 11.115 | 8756.0 | 8594.484 | 3.27 | 13,287.0 | 13,029.839 | 7.665 |
ELIT_SINE | 48,313.0 | 46,879.742 | 11.357 | 8746.0 | 8597.0 | 3.38 | 13,286.0 | 13,014.065 | 7.672 |
ELIT_SINGER | 48,866.0 | 46,692.613 | 10.343 | 8798.0 | 8596.032 | 2.806 | 13,285.0 | 13,063.516 | 7.679 |
ELIT_SINU | 49,053.0 | 46,605.419 | 9.999 | 8706.0 | 8586.774 | 3.822 | 13,287.0 | 13,051.581 | 7.665 |
ELIT_TENT | 49,839.0 | 46,487.742 | 8.557 | 8720.0 | 8586.871 | 3.668 | 13,380.0 | 13,053.387 | 7.019 |
ELIT_CIRCLE | 49,340.0 | 47,225.548 | 9.473 | 8808.0 | 8600.032 | 2.696 | 13,390.0 | 12,989.129 | 6.949 |
Experiment | knapPI_1_200_1000_1 | knapPI_2_200_1000_1 | knapPI_3_200_1000_1 | ||||||
Best | Avg. | RPD | Best | Avg. | RPD | Best | Avg. | RPD | |
STD | 105,363.0 | 103,724.323 | 4.757 | 17,794.0 | 17,663.065 | 1.424 | 27,716.0 | 27,517.065 | 4.16 |
STD_LOG | 102,554.0 | 101,476.903 | 7.296 | 17,643.0 | 17,506.129 | 2.26 | 27,214.0 | 26,996.968 | 5.896 |
STD_PIECE | 105,728.0 | 103,444.581 | 4.427 | 17,757.0 | 17,658.323 | 1.629 | 27,619.0 | 27,488.613 | 4.495 |
STD_SINE | 103,910.0 | 102,593.613 | 6.07 | 17,736.0 | 17,631.355 | 1.745 | 27,418.0 | 27,308.677 | 5.19 |
STD_SINGER | 95,257.0 | 90,910.032 | 13.892 | 17,005.0 | 16,811.968 | 5.795 | 25,618.0 | 25,265.516 | 11.415 |
STD_SINU | 95,017.0 | 91,056.871 | 14.109 | 17,111.0 | 16,776.548 | 5.207 | 26,012.0 | 25,404.613 | 10.052 |
STD_TENT | 106,046.0 | 104,096.097 | 4.139 | 17,773.0 | 17,651.452 | 1.54 | 27,814.0 | 27,548.613 | 3.821 |
STD_CIRCLE | 108,845.0 | 108,422.226 | 1.609 | 17,974.0 | 17,939.097 | 0.427 | 28,518.0 | 28,371.161 | 1.387 |
COM | 94,027.0 | 90,608.0 | 15.004 | 17,009.0 | 16,747.903 | 5.773 | 25,908.0 | 25,323.065 | 10.412 |
COM_LOG | 95,094.0 | 90,690.839 | 14.039 | 16,964.0 | 16,711.581 | 6.022 | 25,917.0 | 25,344.71 | 10.381 |
COM_PIECE | 94,640.0 | 90,199.355 | 14.45 | 16,946.0 | 16,682.645 | 6.122 | 26,211.0 | 25,345.065 | 9.364 |
COM_SINE | 95,557.0 | 90,575.968 | 13.621 | 16,982.0 | 16,704.258 | 5.922 | 26,014.0 | 25,301.161 | 10.045 |
COM_SINGER | 94,604.0 | 90,331.581 | 14.482 | 16,906.0 | 16,694.161 | 6.343 | 26,314.0 | 25,326.645 | 9.008 |
COM_SINU | 94,238.0 | 90,794.581 | 14.813 | 16,980.0 | 16,732.581 | 5.933 | 26,004.0 | 25,329.581 | 10.08 |
COM_TENT | 95,329.0 | 90,429.548 | 13.827 | 16,965.0 | 16,707.903 | 6.016 | 25,705.0 | 25,348.677 | 11.114 |
COM_CIRCLE | 93,304.0 | 90,315.484 | 15.657 | 16,954.0 | 16,701.032 | 6.077 | 25,714.0 | 25,337.935 | 11.083 |
ELIT | 93,627.0 | 90,490.226 | 15.365 | 17,042.0 | 16,727.0 | 5.59 | 25,819.0 | 25,238.839 | 10.72 |
ELIT_LOG | 94,817.0 | 90,709.839 | 14.29 | 17,005.0 | 16,725.839 | 5.795 | 25,914.0 | 25,278.226 | 10.391 |
ELIT_PIECE | 94,780.0 | 91,059.161 | 14.323 | 16,950.0 | 16,734.0 | 6.099 | 25,719.0 | 25,284.065 | 11.065 |
ELIT_SINE | 95,798.0 | 90,960.581 | 13.403 | 17,063.0 | 16,706.323 | 5.473 | 25,705.0 | 25,235.161 | 11.114 |
ELIT_SINGER | 95,383.0 | 90,819.161 | 13.778 | 16,993.0 | 16,677.323 | 5.861 | 25,616.0 | 25,309.645 | 11.422 |
ELIT_SINU | 96,188.0 | 90,429.774 | 13.05 | 16,840.0 | 16,678.774 | 6.709 | 25,915.0 | 25,287.871 | 10.388 |
ELIT_TENT | 95,551.0 | 91,256.774 | 13.626 | 17,056.0 | 16,724.581 | 5.512 | 26,111.0 | 25,325.871 | 9.71 |
ELIT_CIRCLE | 94,775.0 | 90,491.323 | 14.328 | 16,972.0 | 16,737.226 | 5.978 | 25,816.0 | 25,341.065 | 10.73 |
Experiment | GWO | WOA | SCA | TOTAL | Experiment | GWO | WOA | SCA | TOTAL |
---|---|---|---|---|---|---|---|---|---|
STD | 8/23 | 8/23 | 8/23 | 24/69 | COM_SINE | 6/23 | 1/23 | 1/23 | 8/69 |
STD_LOG | 8/23 | 8/23 | 8/23 | 24/69 | COM_LOG | 2/23 | 0/23 | 0/23 | 2/69 |
STD_PIECE | 8/23 | 8/23 | 8/23 | 24/69 | COM_SINGER | 0/23 | 0/23 | 0/23 | 0/69 |
STD_SINE | 8/23 | 8/23 | 8/23 | 24/69 | COM_SINU | 0/23 | 0/23 | 0/23 | 0/69 |
STD_TENT | 8/23 | 8/23 | 8/23 | 24/69 | ELIT | 0/23 | 0/23 | 0/23 | 0/69 |
STD_CIRCLE | 8/23 | 8/23 | 8/23 | 24/69 | ELIT_LOG | 0/23 | 0/23 | 0/23 | 0/69 |
STD_SINGER | 7/23 | 8/23 | 8/23 | 23/69 | ELIT_PIECE | 0/23 | 0/23 | 0/23 | 0/69 |
COM_CIRCLE | 6/23 | 8/23 | 8/23 | 22/69 | ELIT_SINE | 0/23 | 0/23 | 0/23 | 0/69 |
COM | 5/23 | 8/23 | 8/23 | 21/69 | ELIT_SINGER | 0/23 | 0/23 | 0/23 | 0/69 |
COM_PIECE | 6/23 | 6/23 | 6/23 | 18/69 | ELIT_SINU | 0/23 | 0/23 | 0/23 | 0/69 |
COM_TENT | 2/23 | 8/23 | 8/23 | 18/69 | ELIT_TENT | 0/23 | 0/23 | 0/23 | 0/69 |
STD_SINU | 0/23 | 8/23 | 8/23 | 16/69 | ELIT_CIRCLE | 0/23 | 0/23 | 0/23 | 0/69 |
STD | STD_LOG | STD_PIECE | STD_SINE | STD_SINGER | STD_SINU | STD_TENT | STD_CIRCLE | COM | COM_LOG | COM_PIECE | COM_SINE | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
STD | X | 0.429 | 0.633 | 0.5 | 0.363 | 0.357 | 0.718 | 0.749 | 0.239 | 0.215 | 0.226 | 0.156 |
STD_LOG | 1.0 | X | 1.0 | 0.993 | 0.363 | 0.357 | 1.0 | 0.786 | 0.239 | 0.215 | 0.226 | 0.156 |
STD_PIECE | 0.797 | 0.429 | X | 0.5 | 0.363 | 0.357 | 0.748 | 0.765 | 0.239 | 0.215 | 0.226 | 0.156 |
STD_SINE | 0.928 | 0.435 | 1.0 | X | 0.363 | 0.357 | 0.929 | 0.786 | 0.239 | 0.215 | 0.226 | 0.156 |
STD_SINGER | 0.995 | 0.995 | 0.995 | 0.995 | X | 0.372 | 0.995 | 0.857 | 0.271 | 0.254 | 0.273 | 0.248 |
STD_SINU | 1.0 | 1.0 | 1.0 | 1.0 | 0.985 | X | 1.0 | 0.926 | 0.776 | 0.707 | 0.77 | 0.757 |
STD_TENT | 0.711 | 0.429 | 0.681 | 0.5 | 0.363 | 0.357 | X | 0.784 | 0.239 | 0.215 | 0.226 | 0.156 |
STD_CIRCLE | 0.538 | 0.5 | 0.521 | 0.5 | 0.428 | 0.36 | 0.502 | X | 0.298 | 0.286 | 0.291 | 0.29 |
COM | 0.978 | 0.978 | 0.978 | 0.978 | 0.875 | 0.37 | 0.978 | 0.846 | X | 0.324 | 0.556 | 0.397 |
COM_LOG | 1.0 | 1.0 | 1.0 | 1.0 | 0.89 | 0.437 | 1.0 | 0.857 | 0.892 | X | 0.876 | 0.847 |
COM_PIECE | 0.989 | 0.989 | 0.989 | 0.989 | 0.872 | 0.374 | 0.989 | 0.852 | 0.661 | 0.339 | X | 0.427 |
COM_SINE | 0.988 | 0.988 | 0.988 | 0.988 | 0.897 | 0.387 | 0.988 | 0.853 | 0.75 | 0.297 | 0.72 | X |
COM_SINGER | 1.0 | 1.0 | 1.0 | 1.0 | 0.987 | 0.74 | 1.0 | 0.961 | 0.962 | 0.909 | 0.973 | 0.962 |
COM_SINU | 1.0 | 1.0 | 1.0 | 1.0 | 0.975 | 0.816 | 1.0 | 0.929 | 0.905 | 0.814 | 0.864 | 0.916 |
COM_TENT | 0.984 | 0.984 | 0.984 | 0.984 | 0.948 | 0.424 | 0.984 | 0.849 | 0.667 | 0.335 | 0.608 | 0.476 |
COM_CIRCLE | 0.999 | 0.999 | 0.999 | 0.999 | 0.67 | 0.433 | 0.999 | 0.928 | 0.509 | 0.308 | 0.465 | 0.46 |
ELIT | 1.0 | 1.0 | 1.0 | 1.0 | 0.992 | 0.809 | 1.0 | 1.0 | 0.963 | 0.953 | 0.977 | 0.954 |
ELIT_LOG | 1.0 | 1.0 | 1.0 | 1.0 | 0.949 | 0.719 | 1.0 | 1.0 | 0.94 | 0.878 | 0.937 | 0.968 |
ELIT_PIECE | 1.0 | 1.0 | 1.0 | 1.0 | 0.952 | 0.764 | 1.0 | 1.0 | 0.935 | 0.862 | 0.906 | 0.942 |
ELIT_SINE | 1.0 | 1.0 | 1.0 | 1.0 | 0.966 | 0.812 | 1.0 | 1.0 | 0.93 | 0.896 | 0.951 | 0.943 |
ELIT_SINGER | 1.0 | 1.0 | 1.0 | 1.0 | 0.984 | 0.794 | 1.0 | 1.0 | 0.973 | 0.921 | 0.973 | 0.982 |
ELIT_SINU | 1.0 | 1.0 | 1.0 | 1.0 | 0.986 | 0.824 | 1.0 | 1.0 | 0.977 | 0.89 | 0.975 | 0.984 |
ELIT_TENT | 1.0 | 1.0 | 1.0 | 1.0 | 0.995 | 0.887 | 1.0 | 1.0 | 0.986 | 0.965 | 0.989 | 0.988 |
ELIT_CIRCLE | 1.0 | 1.0 | 1.0 | 1.0 | 0.998 | 0.844 | 1.0 | 1.0 | 0.987 | 0.943 | 0.991 | 0.982 |
STD | 0.143 | 0.214 | 0.16 | 0.216 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_LOG | 0.143 | 0.214 | 0.16 | 0.216 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_PIECE | 0.143 | 0.214 | 0.16 | 0.216 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_SINE | 0.143 | 0.214 | 0.16 | 0.216 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_SINGER | 0.156 | 0.239 | 0.197 | 0.545 | 0.008 | 0.051 | 0.048 | 0.034 | 0.016 | 0.014 | 0.005 | 0.002 |
STD_SINU | 0.405 | 0.4 | 0.721 | 0.782 | 0.192 | 0.283 | 0.238 | 0.19 | 0.208 | 0.178 | 0.115 | 0.158 |
STD_TENT | 0.143 | 0.214 | 0.16 | 0.216 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_CIRCLE | 0.183 | 0.214 | 0.294 | 0.286 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
COM | 0.182 | 0.24 | 0.48 | 0.635 | 0.038 | 0.06 | 0.066 | 0.071 | 0.028 | 0.024 | 0.014 | 0.014 |
COM_LOG | 0.236 | 0.33 | 0.809 | 0.836 | 0.048 | 0.123 | 0.139 | 0.105 | 0.08 | 0.111 | 0.035 | 0.058 |
COM_PIECE | 0.17 | 0.281 | 0.539 | 0.68 | 0.024 | 0.064 | 0.094 | 0.05 | 0.027 | 0.026 | 0.011 | 0.009 |
COM_SINE | 0.181 | 0.227 | 0.672 | 0.684 | 0.047 | 0.032 | 0.059 | 0.058 | 0.018 | 0.016 | 0.013 | 0.018 |
COM_SINGER | X | 0.539 | 0.914 | 0.982 | 0.199 | 0.282 | 0.236 | 0.208 | 0.202 | 0.198 | 0.095 | 0.152 |
COM_SINU | 0.606 | X | 0.861 | 0.841 | 0.285 | 0.416 | 0.356 | 0.283 | 0.281 | 0.243 | 0.16 | 0.23 |
COM_TENT | 0.229 | 0.283 | X | 0.677 | 0.079 | 0.083 | 0.108 | 0.093 | 0.072 | 0.061 | 0.045 | 0.047 |
COM_CIRCLE | 0.162 | 0.303 | 0.468 | X | 0.001 | 0.051 | 0.083 | 0.023 | 0.01 | 0.012 | 0.004 | 0.004 |
ELIT | 0.802 | 0.717 | 0.922 | 0.999 | X | 0.594 | 0.519 | 0.543 | 0.447 | 0.482 | 0.343 | 0.434 |
ELIT_LOG | 0.72 | 0.586 | 0.917 | 0.95 | 0.41 | X | 0.451 | 0.423 | 0.385 | 0.387 | 0.278 | 0.371 |
ELIT_PIECE | 0.766 | 0.646 | 0.892 | 0.918 | 0.485 | 0.553 | X | 0.441 | 0.368 | 0.425 | 0.284 | 0.407 |
ELIT_SINE | 0.794 | 0.72 | 0.908 | 0.977 | 0.461 | 0.581 | 0.564 | X | 0.459 | 0.47 | 0.311 | 0.416 |
ELIT_SINGER | 0.8 | 0.722 | 0.929 | 0.99 | 0.557 | 0.618 | 0.636 | 0.545 | X | 0.53 | 0.378 | 0.499 |
ELIT_SINU | 0.804 | 0.759 | 0.94 | 0.988 | 0.522 | 0.617 | 0.579 | 0.534 | 0.474 | X | 0.352 | 0.467 |
ELIT_TENT | 0.907 | 0.842 | 0.955 | 0.996 | 0.66 | 0.725 | 0.72 | 0.693 | 0.626 | 0.652 | X | 0.631 |
ELIT_CIRCLE | 0.85 | 0.773 | 0.954 | 0.996 | 0.57 | 0.633 | 0.597 | 0.588 | 0.505 | 0.537 | 0.374 | X |
STD | STD_LOG | STD_PIECE | STD_SINE | STD_SINGER | STD_SINU | STD_TENT | STD_CIRCLE | COM | COM_LOG | COM_PIECE | COM_SINE | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
STD | X | 0.483 | 0.742 | 0.537 | 0.429 | 0.426 | 0.72 | 0.737 | 0.301 | 0.22 | 0.239 | 0.224 |
STD_LOG | 0.947 | X | 0.986 | 0.94 | 0.429 | 0.426 | 0.986 | 0.783 | 0.301 | 0.22 | 0.239 | 0.224 |
STD_PIECE | 0.761 | 0.443 | X | 0.506 | 0.429 | 0.426 | 0.796 | 0.777 | 0.301 | 0.22 | 0.239 | 0.224 |
STD_SINE | 0.964 | 0.49 | 0.995 | X | 0.429 | 0.426 | 0.99 | 0.786 | 0.301 | 0.22 | 0.239 | 0.224 |
STD_SINGER | 1.0 | 1.0 | 1.0 | 1.0 | X | 0.497 | 1.0 | 0.857 | 0.301 | 0.22 | 0.239 | 0.224 |
STD_SINU | 0.932 | 0.932 | 0.932 | 0.932 | 0.861 | X | 0.932 | 0.789 | 0.232 | 0.152 | 0.17 | 0.155 |
STD_TENT | 0.782 | 0.444 | 0.777 | 0.511 | 0.429 | 0.426 | X | 0.754 | 0.301 | 0.22 | 0.239 | 0.224 |
STD_CIRCLE | 0.692 | 0.574 | 0.652 | 0.643 | 0.5 | 0.497 | 0.675 | X | 0.36 | 0.289 | 0.298 | 0.289 |
COM | 0.986 | 0.986 | 0.986 | 0.986 | 0.986 | 0.984 | 0.986 | 0.926 | X | 0.258 | 0.545 | 0.411 |
COM_LOG | 0.994 | 0.994 | 0.994 | 0.994 | 0.994 | 0.992 | 0.994 | 0.926 | 0.958 | X | 0.933 | 0.852 |
COM_PIECE | 0.978 | 0.978 | 0.978 | 0.978 | 0.978 | 0.975 | 0.978 | 0.917 | 0.675 | 0.284 | X | 0.458 |
COM_SINE | 0.991 | 0.991 | 0.991 | 0.991 | 0.991 | 0.989 | 0.991 | 0.925 | 0.806 | 0.365 | 0.76 | X |
COM_SINGER | 0.995 | 0.995 | 0.995 | 0.995 | 0.995 | 0.992 | 0.995 | 0.929 | 0.96 | 0.873 | 0.93 | 0.896 |
COM_SINU | 0.997 | 0.997 | 0.997 | 0.997 | 0.997 | 0.997 | 0.997 | 0.925 | 0.91 | 0.777 | 0.865 | 0.819 |
COM_TENT | 0.978 | 0.978 | 0.978 | 0.978 | 0.978 | 0.976 | 0.978 | 0.918 | 0.648 | 0.249 | 0.552 | 0.388 |
COM_CIRCLE | 0.989 | 0.989 | 0.989 | 0.989 | 0.989 | 0.986 | 0.989 | 0.928 | 0.47 | 0.297 | 0.358 | 0.315 |
ELIT | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 0.989 | 0.902 | 0.959 | 0.923 |
ELIT_LOG | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 0.986 | 0.902 | 0.963 | 0.933 |
ELIT_PIECE | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 0.967 | 0.913 | 0.94 | 0.925 |
ELIT_SINE | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 0.993 | 0.92 | 0.969 | 0.948 |
ELIT_SINGER | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 0.993 | 0.93 | 0.971 | 0.945 |
ELIT_SINU | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 0.999 | 0.921 | 0.994 | 0.959 |
ELIT_TENT | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 0.978 | 0.911 | 0.948 | 0.932 |
ELIT_CIRCLE | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 0.991 | 0.91 | 0.977 | 0.946 |
STD | 0.149 | 0.146 | 0.31 | 0.226 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_LOG | 0.149 | 0.146 | 0.31 | 0.226 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_PIECE | 0.149 | 0.146 | 0.31 | 0.226 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_SINE | 0.149 | 0.146 | 0.31 | 0.226 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_SINGER | 0.149 | 0.146 | 0.31 | 0.226 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_SINU | 0.08 | 0.146 | 0.241 | 0.158 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_TENT | 0.149 | 0.146 | 0.31 | 0.226 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_CIRCLE | 0.214 | 0.146 | 0.369 | 0.286 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
COM | 0.184 | 0.163 | 0.642 | 0.746 | 0.011 | 0.014 | 0.033 | 0.008 | 0.007 | 0.001 | 0.023 | 0.009 |
COM_LOG | 0.271 | 0.297 | 0.966 | 0.847 | 0.099 | 0.099 | 0.087 | 0.081 | 0.071 | 0.08 | 0.089 | 0.091 |
COM_PIECE | 0.215 | 0.209 | 0.667 | 0.788 | 0.042 | 0.038 | 0.06 | 0.031 | 0.029 | 0.007 | 0.053 | 0.023 |
COM_SINE | 0.248 | 0.255 | 0.829 | 0.83 | 0.077 | 0.067 | 0.075 | 0.053 | 0.056 | 0.042 | 0.068 | 0.055 |
COM_SINGER | X | 0.438 | 0.942 | 0.922 | 0.162 | 0.199 | 0.198 | 0.174 | 0.101 | 0.119 | 0.153 | 0.179 |
COM_SINU | 0.635 | X | 0.922 | 0.863 | 0.281 | 0.274 | 0.263 | 0.232 | 0.188 | 0.206 | 0.245 | 0.249 |
COM_TENT | 0.202 | 0.152 | X | 0.738 | 0.033 | 0.016 | 0.043 | 0.014 | 0.012 | 0.006 | 0.032 | 0.008 |
COM_CIRCLE | 0.223 | 0.21 | 0.479 | X | 0.013 | 0.009 | 0.036 | 0.009 | 0.006 | 0.001 | 0.017 | 0.003 |
ELIT | 0.84 | 0.721 | 0.968 | 0.987 | X | 0.474 | 0.433 | 0.39 | 0.386 | 0.358 | 0.434 | 0.377 |
ELIT_LOG | 0.802 | 0.728 | 0.984 | 0.991 | 0.53 | X | 0.514 | 0.442 | 0.422 | 0.438 | 0.444 | 0.399 |
ELIT_PIECE | 0.804 | 0.739 | 0.958 | 0.964 | 0.572 | 0.49 | X | 0.412 | 0.446 | 0.452 | 0.442 | 0.423 |
ELIT_SINE | 0.828 | 0.769 | 0.986 | 0.992 | 0.614 | 0.563 | 0.593 | X | 0.495 | 0.544 | 0.494 | 0.499 |
ELIT_SINGER | 0.9 | 0.813 | 0.988 | 0.994 | 0.619 | 0.582 | 0.558 | 0.509 | X | 0.487 | 0.514 | 0.483 |
ELIT_SINU | 0.882 | 0.796 | 0.994 | 0.999 | 0.646 | 0.567 | 0.552 | 0.46 | 0.518 | X | 0.529 | 0.455 |
ELIT_TENT | 0.849 | 0.757 | 0.969 | 0.983 | 0.569 | 0.56 | 0.562 | 0.509 | 0.49 | 0.475 | X | 0.488 |
ELIT_CIRCLE | 0.822 | 0.753 | 0.992 | 0.997 | 0.626 | 0.605 | 0.581 | 0.506 | 0.521 | 0.548 | 0.516 | X |
STD | STD_LOG | STD_PIECE | STD_SINE | STD_SINGER | STD_SINU | STD_TENT | STD_CIRCLE | COM | COM_LOG | COM_PIECE | COM_SINE | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
STD | X | 0.429 | 0.637 | 0.543 | 0.369 | 0.21 | 0.869 | 0.857 | 0.143 | 0.143 | 0.143 | 0.143 |
STD_LOG | 1.0 | X | 1.0 | 1.0 | 0.369 | 0.21 | 1.0 | 0.881 | 0.143 | 0.143 | 0.143 | 0.143 |
STD_PIECE | 0.794 | 0.429 | X | 0.562 | 0.369 | 0.21 | 0.876 | 0.857 | 0.143 | 0.143 | 0.143 | 0.143 |
STD_SINE | 0.886 | 0.429 | 0.867 | X | 0.369 | 0.21 | 0.86 | 0.857 | 0.143 | 0.143 | 0.143 | 0.143 |
STD_SINGER | 0.989 | 0.989 | 0.989 | 0.989 | X | 0.36 | 0.989 | 0.918 | 0.223 | 0.24 | 0.2 | 0.222 |
STD_SINU | 0.935 | 0.935 | 0.935 | 0.935 | 0.785 | X | 0.935 | 0.863 | 0.492 | 0.498 | 0.438 | 0.494 |
STD_TENT | 0.561 | 0.429 | 0.554 | 0.569 | 0.369 | 0.21 | X | 0.857 | 0.143 | 0.143 | 0.143 | 0.143 |
STD_CIRCLE | 0.5 | 0.476 | 0.5 | 0.5 | 0.369 | 0.21 | 0.5 | X | 0.212 | 0.172 | 0.214 | 0.202 |
COM | 1.0 | 1.0 | 1.0 | 1.0 | 0.92 | 0.582 | 1.0 | 0.93 | X | 0.513 | 0.458 | 0.678 |
COM_LOG | 1.0 | 1.0 | 1.0 | 1.0 | 0.903 | 0.576 | 1.0 | 0.971 | 0.632 | X | 0.464 | 0.673 |
COM_PIECE | 1.0 | 1.0 | 1.0 | 1.0 | 0.944 | 0.636 | 1.0 | 0.928 | 0.688 | 0.681 | X | 0.771 |
COM_SINE | 1.0 | 1.0 | 1.0 | 1.0 | 0.921 | 0.579 | 1.0 | 0.941 | 0.468 | 0.473 | 0.374 | X |
COM_SINGER | 1.0 | 1.0 | 1.0 | 1.0 | 0.947 | 0.847 | 1.0 | 1.0 | 0.914 | 0.907 | 0.796 | 0.906 |
COM_SINU | 1.0 | 1.0 | 1.0 | 1.0 | 0.895 | 0.839 | 1.0 | 0.929 | 0.692 | 0.677 | 0.595 | 0.704 |
COM_TENT | 1.0 | 1.0 | 1.0 | 1.0 | 0.926 | 0.605 | 1.0 | 0.93 | 0.609 | 0.52 | 0.454 | 0.699 |
COM_CIRCLE | 1.0 | 1.0 | 1.0 | 1.0 | 0.924 | 0.691 | 1.0 | 0.987 | 0.734 | 0.704 | 0.596 | 0.754 |
ELIT | 1.0 | 1.0 | 1.0 | 1.0 | 0.963 | 0.858 | 1.0 | 1.0 | 0.905 | 0.892 | 0.798 | 0.865 |
ELIT_LOG | 1.0 | 1.0 | 1.0 | 1.0 | 0.942 | 0.808 | 1.0 | 1.0 | 0.83 | 0.831 | 0.722 | 0.837 |
ELIT_PIECE | 1.0 | 1.0 | 1.0 | 1.0 | 0.899 | 0.844 | 1.0 | 1.0 | 0.84 | 0.83 | 0.764 | 0.831 |
ELIT_SINE | 1.0 | 1.0 | 1.0 | 1.0 | 0.934 | 0.838 | 1.0 | 1.0 | 0.868 | 0.88 | 0.779 | 0.875 |
ELIT_SINGER | 1.0 | 1.0 | 1.0 | 1.0 | 0.912 | 0.832 | 1.0 | 1.0 | 0.825 | 0.847 | 0.754 | 0.856 |
ELIT_SINU | 1.0 | 1.0 | 1.0 | 1.0 | 0.95 | 0.854 | 1.0 | 1.0 | 0.901 | 0.909 | 0.82 | 0.885 |
ELIT_TENT | 1.0 | 1.0 | 1.0 | 1.0 | 0.878 | 0.844 | 1.0 | 1.0 | 0.819 | 0.816 | 0.75 | 0.795 |
ELIT_CIRCLE | 1.0 | 1.0 | 1.0 | 1.0 | 0.927 | 0.854 | 1.0 | 1.0 | 0.882 | 0.861 | 0.786 | 0.872 |
STD | 0.143 | 0.143 | 0.143 | 0.143 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_LOG | 0.143 | 0.143 | 0.143 | 0.143 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_PIECE | 0.143 | 0.143 | 0.143 | 0.143 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_SINE | 0.143 | 0.143 | 0.143 | 0.143 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_SINGER | 0.196 | 0.248 | 0.217 | 0.219 | 0.037 | 0.059 | 0.102 | 0.066 | 0.088 | 0.051 | 0.123 | 0.073 |
STD_SINU | 0.227 | 0.306 | 0.469 | 0.383 | 0.144 | 0.193 | 0.158 | 0.163 | 0.17 | 0.148 | 0.158 | 0.147 |
STD_TENT | 0.143 | 0.143 | 0.143 | 0.143 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
STD_CIRCLE | 0.143 | 0.143 | 0.213 | 0.157 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
COM | 0.23 | 0.381 | 0.538 | 0.411 | 0.096 | 0.173 | 0.161 | 0.134 | 0.177 | 0.1 | 0.182 | 0.12 |
COM_LOG | 0.238 | 0.396 | 0.626 | 0.442 | 0.11 | 0.171 | 0.172 | 0.122 | 0.155 | 0.092 | 0.186 | 0.14 |
COM_PIECE | 0.349 | 0.478 | 0.693 | 0.549 | 0.203 | 0.279 | 0.237 | 0.223 | 0.247 | 0.181 | 0.251 | 0.216 |
COM_SINE | 0.239 | 0.37 | 0.448 | 0.391 | 0.136 | 0.165 | 0.17 | 0.126 | 0.146 | 0.116 | 0.206 | 0.129 |
COM_SINGER | X | 0.591 | 0.868 | 0.798 | 0.283 | 0.382 | 0.329 | 0.29 | 0.354 | 0.281 | 0.336 | 0.283 |
COM_SINU | 0.482 | X | 0.65 | 0.596 | 0.256 | 0.341 | 0.313 | 0.292 | 0.293 | 0.304 | 0.316 | 0.267 |
COM_TENT | 0.276 | 0.423 | X | 0.426 | 0.165 | 0.208 | 0.19 | 0.16 | 0.168 | 0.147 | 0.211 | 0.145 |
COM_CIRCLE | 0.347 | 0.477 | 0.72 | X | 0.147 | 0.184 | 0.165 | 0.129 | 0.163 | 0.128 | 0.206 | 0.132 |
ELIT | 0.719 | 0.747 | 0.836 | 0.854 | X | 0.633 | 0.608 | 0.527 | 0.671 | 0.616 | 0.564 | 0.526 |
ELIT_LOG | 0.621 | 0.662 | 0.794 | 0.817 | 0.372 | X | 0.511 | 0.376 | 0.514 | 0.469 | 0.426 | 0.425 |
ELIT_PIECE | 0.674 | 0.69 | 0.812 | 0.836 | 0.395 | 0.492 | X | 0.409 | 0.531 | 0.437 | 0.48 | 0.396 |
ELIT_SINE | 0.713 | 0.711 | 0.842 | 0.872 | 0.477 | 0.628 | 0.595 | X | 0.612 | 0.577 | 0.528 | 0.511 |
ELIT_SINGER | 0.649 | 0.71 | 0.833 | 0.838 | 0.332 | 0.491 | 0.473 | 0.392 | X | 0.442 | 0.445 | 0.379 |
ELIT_SINU | 0.722 | 0.699 | 0.854 | 0.874 | 0.387 | 0.535 | 0.566 | 0.426 | 0.562 | X | 0.473 | 0.42 |
ELIT_TENT | 0.667 | 0.686 | 0.79 | 0.795 | 0.44 | 0.579 | 0.524 | 0.476 | 0.559 | 0.531 | X | 0.484 |
ELIT_CIRCLE | 0.719 | 0.736 | 0.857 | 0.87 | 0.478 | 0.579 | 0.608 | 0.493 | 0.625 | 0.584 | 0.52 | X |
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Cisternas-Caneo, F.; Crawford, B.; Soto, R.; Giachetti, G.; Paz, Á.; Peña Fritz, A. Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics. Mathematics 2024, 12, 262. https://doi.org/10.3390/math12020262
Cisternas-Caneo F, Crawford B, Soto R, Giachetti G, Paz Á, Peña Fritz A. Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics. Mathematics. 2024; 12(2):262. https://doi.org/10.3390/math12020262
Chicago/Turabian StyleCisternas-Caneo, Felipe, Broderick Crawford, Ricardo Soto, Giovanni Giachetti, Álex Paz, and Alvaro Peña Fritz. 2024. "Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics" Mathematics 12, no. 2: 262. https://doi.org/10.3390/math12020262